Scaling laws in granular flow and pedestrian flow

Abstract

We use particle-based simulations to examine the flow of particles through an exit. Simulations involve both gravity-driven particles (representing granular material) and velocity-driven particles (mimicking pedestrian dynamics). Contact forces between particles include elastic, viscous, and frictional forces; and simulations use bunker geometry. Power laws are observed in the relation between flow rate and exit width. Simulations of granular flow showed that the power law has little dependence on the coefficient of friction. Polydisperse granular systems produced higher flow rates than those produced by monodisperse ones. We extend the particle model to include the main features of pedestrian dynamics: thoracic shape, shoulder rotation, and desired velocity oriented towards the exit. Higher desired velocity resulted in higher flow rate. Granular simulations always give higher flow rate than pedestrian simulations, despite the values of aspect ratio of the particles. In terms of force distribution, pedestrians and granulates share similar properties with the non-democratic distribution of forces that poses high risks of injuries in a bottleneck situation.